Question

the ratio of the area of two Triangles is equal to the square of the ratio of their corresponding sides

Answer 1

Theorem = The ratio of area of any two similar triangles is equal to the ratio of square of their corresponding sides.


KEY POINTS TO REMEMBER :-

Step 1 = Take two similar triangles as given.

Step 2 = prove the corresponding sides equal by similarity.

Step 3 = Draw altitudes in both the triangles and prove any small triangle similar to another small triangle containing altitudes.

Step 4 = prove that the ratio of altitudes is equal to ratio of one corresponding side by similarity of two small triangles.

Step 5 = find areas and then their ratios.

Step 6 = replace the ratio of altitudes and sides to any one same side.

Step 7 = The answer is derived with only one corresponding sides.

Step 8 = using step 2, replace the sides one by one and get all the ratio of corresponding side's square equal to the ratio of areas.



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